If he was Jesus it would be a bit over the top to start a quest just to find his cup, wouldn’t it? I mean he’d be making cabinets and things.
Nah. You see, Arthur didn’t go looking for the Grail. He just sent his other knights out looking for it. Which he knew was a futile quest, what with the Grail being there in the kitchen as a waterbowl for his cat, Mr. Fuzzybritches. Thus he could send out annoying followers on an “important mission” and know that they’d be away and out of his hair for a goodly while. Look at who he sent out: the most ultra-pious, chaste, holier-than-thou knights. Who would want those guys lurking about Camelot spoiling all the fun with the ale and the games with the wenches?
And that would give him more free time to head up north and go bowling with Ol’ Muckle Alex.